HARMONIC ANALYSIS AND PREDICTION OF TIDES. 139 



set of constants, one for the north components and the other for the 

 east components. 



Although the predicting machine was designed, primarily, for the 

 prediction of the tides, it is adapted also to the prediction of tidal 

 currents. The currents involve both direction and velocity, while 

 the tides involve height only. The predicting machine can not be 

 used directly for the determination of direction, but it is used for 

 the summation of component velocities in the same manner as for 

 the summation of component heights in the prediction of the tides. 



It is therefore directly applicable for the reversing type of current, 

 in which only a single direction need be considered, the velocities 

 being taken as positive or negative according to the direction in 

 which it is flowing. 



For the rotary type of current all velocities might be resolved into 

 two directions at right angles to each other, such as the north and 

 €!ast, and velocity predictions made for each of these directions inde- 

 pendently. The labor, however, of recombining the north and east 

 components into the resultant velocities would be practically pro- 

 hibitive without a machine especially designed for this purpose. 



For the predictions of the reversing current two methods are 

 employed. The first is of general application and requires that the 

 harmonic constants of the current components be obtained from an 

 analysis of the current velocities. The machine settings are then 

 computed in the same manner as for the prediction of the tides 

 and using the same forms with slight modifications in the headings, 

 the amplitudes being expressed in knots instead of feet. The approxi- 

 mate extreme range will be taken as twice the maximum current in 

 one direction. The height dial unit will be taken as the knot instead 

 of the foot, and zero velocity will be taken to correspond to mean 

 sea level. 



If the machine is now set up and operated in the same manner as 

 for the prediction of tides, the current velocities may be read directly 

 from the face of the machine for any desired time, the positive values 

 being for the velocities in the direction originally adopted as positive, 

 preferably the flood current, and the negative values for the velocities 

 in the opposite direction. The machine will be automatically stopped 

 at each maximum flood and ebb current, and slack water will be 

 indicated by the zero position of the recording hand. The velocity 

 of the current for any desired time and the times of maximum veloci- 

 ties and of slack water may be also obtained from the predicted curve. 



A second method of predicting the reversing current, which is 

 more indirect than that just described, is applicable to a hydraulic 

 current in a strait. Such a current is caused by the difference in 

 the head of the tidal waters at the two ends of the strait. Except 

 for the lag due to the inertia or momentum of the water, slack would 

 occur at the time the water is at the same level at both ends and the 

 maximum velocities at the times of greatest difference in the head. 

 For this method of predicting it is necessary that tidal harmonic 

 constants should be available for both ends of the strait. 



Let these ends be designated by M and N, and let the single sub- 

 script refer to the tidal constants at M and the double subscript to 

 those at iV, and for convenience call the direction of flow from' M to 

 N as flood or positive and the reverse direction as ebb or negative. 



72934— 24t 10 



